2018
Том 70
№ 11

All Issues

Finkelshtein D. L.

Articles: 2
Article (Ukrainian)

On convolutions on configuration spaces. II. spaces of locally finite configurations

Finkelshtein D. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1699-1719

We consider the convolution of probability measures on spaces of locally finite configurations (subsets of a phase space) as well as their connection with the convolution of the corresponding correlation measures and functionals. In particular,the convolution of Gibbs measures is studied. We also describe a relationship between invariant measures with respect to some operator and properties of the corresponding image of this operator on correlation functions.

Article (Ukrainian)

On convolutions on configuration spaces. I. Spaces of finite configurations

Finkelshtein D. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1547-1567

We consider two types of convolutions ($\ast$ and $\star$) of functions on spaces of finite configurations (finite subsets of a phase space) and study some of their properties. A relationship between the $\ast$-convolution and the convolution of measures on spaces of finite configurations is described. Properties of the operators of multiplication and differentiation with respect to the $\ast$-convolution are investigated. We also present conditions under which the $\ast$-convolution is positive definite with respect to the $\star$-convolution.